Monthly Archives: December 2017

Exterior Algebra

Interior Antiderivations If is a vector space then any form extends to a unique anti-derivation of the exterior algebra , i.e., for homogenous If is a basis of V, the dual basis and if denotes we have the following action on monomials (The sign is negative if the number of terms preceding the matching one… Read More »

Orthogonal Overview

Overview Orthogonal Group is a symmetry group of a vector space equipped with a (non-degenerate) scalar product that is a group of linear transformations such that . If we present as a matrix with respect to some vector basis then is orthogonal when its coefficients satisfy certain algebraic equations which depend on how the basic… Read More »

References

Reps of Lie Algebras & PDEs by Xu V. Kac Lecture Notes Samelson Lecture Notes Baez Octonions Zuber Home Stienstra Lecture Notes on Hypergeometric Structures